We consider the Dirichlet Laplacian $H_gamma$ on a 3D twisted waveguide with random Anderson-type twisting $gamma$. We introduce the integrated density of states $N_gamma$ for the operator $H_gamma$, and investigate the Lifshits tails of $N_gamma$, i.e. the asymptotic behavior of $N_gamma(E)$ as $E downarrow inf {rm supp}, dN_gamma$. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.
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